Problem: Recently Duff has been a soldier in the army. Malek is her commander.

Their country, Andarz Gu has n cities (numbered from 1 to n) and n - 1 bidirectional roads. Each road connects two different cities. There exist a unique path between any two cities.

There are also m people living in Andarz Gu (numbered from 1 to m). Each person has and ID number. ID number of i - th person is i and he/she lives in city number ci. Note that there may be more than one person in a city, also there may be no people living in the city.

<image>

Malek loves to order. That's why he asks Duff to answer to q queries. In each query, he gives her numbers v, u and a.

To answer a query:

Assume there are x people living in the cities lying on the path from city v to city u. Assume these people's IDs are p1, p2, ..., px in increasing order. 

If k = min(x, a), then Duff should tell Malek numbers k, p1, p2, ..., pk in this order. In the other words, Malek wants to know a minimums on that path (or less, if there are less than a people).

Duff is very busy at the moment, so she asked you to help her and answer the queries.

Input

The first line of input contains three integers, n, m and q (1 ≤ n, m, q ≤ 105).

The next n - 1 lines contain the roads. Each line contains two integers v and u, endpoints of a road (1 ≤ v, u ≤ n, v ≠ u).

Next line contains m integers c1, c2, ..., cm separated by spaces (1 ≤ ci ≤ n for each 1 ≤ i ≤ m).

Next q lines contain the queries. Each of them contains three integers, v, u and a (1 ≤ v, u ≤ n and 1 ≤ a ≤ 10).

Output

For each query, print numbers k, p1, p2, ..., pk separated by spaces in one line.

Examples

Input

5 4 5
1 3
1 2
1 4
4 5
2 1 4 3
4 5 6
1 5 2
5 5 10
2 3 3
5 3 1


Output

1 3
2 2 3
0
3 1 2 4
1 2

Note

Graph of Andarz Gu in the sample case is as follows (ID of people in each city are written next to them):

<image>

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

/**
 * Created by hama_du on 15/10/17.
 */
public class C {
    private static final int INF = 114514;

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n = in.nextInt();
        int m = in.nextInt();
        int q = in.nextInt();
        int[][] graph = buildGraph(in, n, n-1);

        int[][] voke = new int[n][10];
        for (int i = 0; i < n ; i++) {
            Arrays.fill(voke[i], INF);
        }
        int[] cn = new int[n];
        for (int i = 0; i < m ; i++) {
            int cid = in.nextInt()-1;
            if (cn[cid] >= 10) {
            } else {
                voke[cid][cn[cid]++] = i+1;
            }
        }

        LCA lca = new LCA(graph, voke);

        while (--q >= 0) {
            int v = in.nextInt()-1;
            int u = in.nextInt()-1;
            int a = in.nextInt();
            int[] res = lca.lca(u, v);

            int cnt = 0;
            for (int i = 0; i < a ; i++) {
                if (res[i] == INF) {
                    continue;
                }
                cnt++;
            }
            out.print(cnt);
            for (int i = 0; i < a ; i++) {
                if (res[i] == INF) {
                    continue;
                }
                out.print(' ');
                out.print(res[i]);
            }
            out.println();
        }


        out.flush();
    }

    static class LCA {
        int[][] graph;
        int[][] parent;
        int[][][] voke;
        int[] depth;

        public LCA(int[][] graph, int[][] nums) {
            int n = graph.length;
            this.graph = graph;
            this.voke = new int[20][n][];
            this.voke[0] = nums;
            init(n);
        }

        void dfs(int now, int from, int dep) {
            parent[0][now] = from;
            depth[now] = dep;
            for (int to : graph[now]) {
                if (to != from) {
                    dfs(to, now, dep+1);
                }
            }
        }

        void init(int n) {
            int log = 1;
            int nn = n;
            while (nn >= 1) {
                nn /= 2;
                log++;
            }
            parent = new int[log+1][n];
            for (int i = 0 ; i <= log ; i++) {
                Arrays.fill(parent[i], -1);
            }
            depth = new int[n];

            dfs(0, -1, 0);

            for (int k = 0 ; k < log ; k++) {
                for (int v = 0 ; v < n ; v++) {
                    if (parent[k][v] < 0) {
                        parent[k+1][v] = -1;
                        voke[k+1][v] = voke[k][v];
                    } else {
                        parent[k+1][v] = parent[k][parent[k][v]];
                        voke[k+1][v] = merge(voke[k][v], voke[k][parent[k][v]]);
                    }
                }
            }

        }

        private int[] merge(int[] a1, int[] a2) {
            int[] res = new int[20];
            for (int i = 0; i < 10 ; i++) {
                res[i] = a1[i];
                res[10+i] = a2[i];
            }
            Arrays.sort(res);
            return Arrays.copyOf(res, 10);
        }

        int[] lca(int u, int v) {
            int loglen = parent.length;
            if (depth[u] > depth[v]) {
                int tmp = u;
                u = v;
                v = tmp;
            }

            int[] res = new int[10];
            Arrays.fill(res, INF);

            for (int k = 0 ; k < loglen ; k++) {
                if (((depth[v] - depth[u]) >> k) % 2 == 1) {
                    res = merge(res, voke[k][v]);
                    v = parent[k][v];
                }
            }
            if (u == v) {
                return merge(res, voke[0][u]);
            }

            for (int k = loglen-1 ; k >= 0 ; k--) {
                if (parent[k][u] != parent[k][v]) {
                    res = merge(res, voke[k][u]);
                    u = parent[k][u];
                    res = merge(res, voke[k][v]);
                    v = parent[k][v];
                }
            }
            return merge(merge(merge(res, voke[0][u]), voke[0][v]), voke[0][parent[0][u]]);
        }
    }

    static int[][] buildGraph(InputReader in, int n, int m) {
        int[][] edges = new int[m][];
        int[][] graph = new int[n][];
        int[] deg = new int[n];
        for (int i = 0 ; i < m ; i++) {
            int a = in.nextInt()-1;
            int b = in.nextInt()-1;
            deg[a]++;
            deg[b]++;
            edges[i] = new int[]{a, b};
        }
        for (int i = 0 ; i < n ; i++) {
            graph[i] = new int[deg[i]];
        }
        for (int i = 0 ; i < m ; i++) {
            int a = edges[i][0];
            int b = edges[i][1];
            graph[a][--deg[a]] = b;
            graph[b][--deg[b]] = a;
        }
        return graph;
    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        private int next() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public char nextChar() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            if ('a' <= c && c <= 'z') {
                return (char) c;
            }
            if ('A' <= c && c <= 'Z') {
                return (char) c;
            }
            throw new InputMismatchException();
        }

        public String nextToken() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            StringBuilder res = new StringBuilder();
            do {
                res.append((char) c);
                c = next();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public int nextInt() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c-'0';
                c = next();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            long sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c-'0';
                c = next();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    static void debug(Object... o) {
        System.err.println(Arrays.deepToString(o));
    }
}